Load identification constitutes an important type of engineering problem. When dealing with the mechanics of deformable objects such as vehicles, machinery, ships, aircraft, installations etc. the knowledge of the actual loads is essential for design and for diagnosis of potential problems. The mechanical load acting on a complex body cannot be measured directly without introducing measuring devices into the test-object into the load-path. The introduction of such devices can change the properties of the test-object, and of the loads working on or within the test-object, and can even be a source of weakness thus rendering such modified test-object unsafe.
In order to overcome this difficulty, inverse analysis in the frequency domain, which estimates dynamic oscillating loads from measured effects resulting from the loads have been studied extensively during the last two decades. Inverse analysis in the frequency domain uses the transfer function matrix between potential loads and the result of these loads; the indicator signals. The transfer function matrix is inverted and multiplied with the spectra of the measured indicator signals. For dynamic loads, an elastic test-object will exhibit characteristic modes or “eigenmodes”. These eigenmodes will have characteristic frequencies. Hence, the response of the test-object will differ depending upon the frequency and the location and direction of the applied loads. This allows the identification of combinations of multiple loads (in direction and in location on the test-object) to be identified.
In practice it is not possible to measure a transfer-function (or transfer-function matrix) from static or 0 Hz upwards. Excitation and sensing needed for transfer-function measurements normally have limitations at lower frequencies, they become excessively expensive and/or in-accurate. Inverse force identification based on transfer functions is therefore limited to highly variable, dynamic and oscillating loads, whose static component is not of interest.
Another well known technique to determine loads is the mount deformation method, where the deformation of flexible element in or on the test-object is measured. The same flexible element can be removed from the test-object, placed on test-bench, and the stiffness matrix can be measured. The combined stiffness and operational deformation will yield the loads in operation; in the frequency domain, or in the time domain including the static load.
Unfortunately there are not always flexible elements at the interface where the loads must be determined, or there are flexible elements but they do not deform enough for a measureable signal, or the deforming part of the test-object cannot be separated from the test-object. So the mount deformation method to determine the static and/or dynamic loads is limited to some special situations.
Another known approach is the inverse strain impulse response method, in which strains are measured on the test-object in operation. Then in a separate test, or analysis, the unaltered test-object in unaltered boundary conditions, is subjected to known or measureable static and possibly also dynamic loads. The strains resulting from these artificial loads are measured as impulse responses. The inverse or reciprocal of these impulse responses is calculated.
The convolution of the impulse responses with the operational strains will yield the loads including the static part of the load.
But the natural boundary conditions will cause reaction forces on the test-object when subjected to the artificial loads. (Objects adrift in space excluded) And these boundary reaction loads can cause the matrix of impulse responses to become singular for the static part (and possibly also at lower frequencies) when multiple loads in natural operating conditions are partially working in the same direction.
In other words, this method will only work when only a few external loads in different directions need to be identified. And, the identification cannot separate the loads and reaction loads from the environment. Multiple loads at multiple locations which are not orthogonal cannot be separated.
The above three methods sometimes also make use of a model of the test-object (analytical or numerical model) instead of measurements to determine the relation between the loads and the indicator signals. This is mostly applicable to test-objects with geometry and materials that can be modelled in a predictable and reliable way. For test-objects that cannot be modelled reliably, an optimization based approach is possible where the model and the loads are updated until a best fit between calculated signals and measured signals is obtained.
Today, in practice, for complex test-objects with multiple loads working on, or within, the test-object in operational conditions, the described state of the art techniques are unsatisfactory for the identification of loads which have an essential static or very low frequency part. The invention provides a solution which allows identification of multiple loads at multiple interfaces, even when these loads are largely or entirely along the same direction. The time signals of these multiple loads, or the spectra can be identified, including the very low frequency or static part.